\documentclass[tikz]{standalone}

%\usepackage{pgf,pgfplots}
%\pgfplotsset{compat=1.17}
%\usepackage{mathrsfs} %provides nicer typesetting of calligraphic letters: $\mathscr{ABC}$
\usetikzlibrary{arrows}

\begin{document}

\definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1cm,y=1cm]
\clip(3,-4) rectangle (12.5,5.5);
\draw [line width=2pt] (5,-0.25)-- (8,-1.25);
\draw [line width=2pt] (8,-2)-- (5,4);
\draw [line width=2pt] (5,4)-- (4.5,6);
\draw [line width=2pt] (8,-1.25)-- (10,-1.5);
\draw [line width=2pt] (8,-2)-- (10,-3);
\draw [line width=2pt] (5,-0.25)-- (4,0.8);
\draw [line width=1pt,dotted,domain=-4:25] plot(\x,{(--42-6*\x)/3});
\draw [line width=1pt,dotted,domain=-4:25] plot(\x,{(--4.25-1*\x)/3});
\draw (3.6,1.8) node[anchor=north west] {$f_{c_1}(t)$};
\draw (8.2,-1.6) node[anchor=north west] {linearization of $f_{c_1}(t)$ at $t'$};
\draw (6.6,-3) node[anchor=north west] {linearization of $f_{c_2}(t)$ at $t'$};
\draw (5.5,4) node[anchor=north west] {$f_{c_2}(t)$};
\draw [line width=1pt,dotted] (5,-7.19114909514104) -- (5,10.176945709892102);
\draw (5,-2) node[anchor=north west] {$t'$};
\draw (3.8,-0.2) node[anchor=north west] {$r_{c_1, t'}$};
\draw (12,0) node[anchor=north west] {$0$};
\draw (7,0.8) node[anchor=north west] {$r_{c_2, t'}=\mbox{score}(c_2)=t_{\max}$};
\draw [line width=1pt,domain=-4:25] plot(\x,{(-0-0*\x)/2});
\draw (4.6,0.7) node[anchor=north west] {$\mbox{score}(c_1)$};
\begin{scriptsize}
\draw [fill=uuuuuu] (7,0) circle (2pt);
\draw [fill=uuuuuu] (4.25,0) circle (2pt);
\draw [fill=uuuuuu] (4.75,0) circle (2pt);
\end{scriptsize}
\end{tikzpicture}
\end{document}